Depends on how old one is talking about. In the first days of D3D or OpenGL, games weren't being written using the fundamental operations, in binary code, that GPUs run on -- it all still needed to be compiled.
In D3D, OGL, and Vulkan, one can choose to compile shaders into binary objects during the build of a project or code it so that it takes place during run time. In turn, these binary objects need to be processed/compiled by the GPU drivers, simply because such objects don't contain the actual micro-op code the processors work with.
I know this is simply a case of semantics, I.e. if a game has been coded in such a way that shader objects are created at run time before the GPU then compiles them, then that could be classed as pre-compilation.
That's actually quite a lot of info to process and check (drivers, multiple OS files, API dlls, game version, all the shaders compiled so far). It's probably just as quick to compile them again.
Without access to exactly how and when a game and the GPU drivers are compiling shaders, it would be very difficult to accurately measure that time period. That said, there will be some differences between the performance of AMD, Intel, and Nvidia's driver compiler but probably not to any degree that would be noticeable to the end user.